Warm-up
¼ + ¼ + ¼ =
½ + ½ =
¾
- ¼ =
 2 5/13 + 7/13 =
Goal/Objective: A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold,
so (51/3)3 must equal 5.
N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
exponents.
Real Life Application
http://www.youtube.com/watch?v=VSgB1IWr6O4
Exponents are used to measure the strength of earthquakes. A level 1 earthquake is 1 x 101 , a level 2
earthquake is 1 x 102, a level 3 is 1 x 103, etc.
Class Discussion
What is the meaning of the expression ? 23
What is the value of the expression 23 ?
How do you know?
Graphic Organizer Distribution
Exponents
5
exponent
3
exponential
base
Example: 125  53 means that 53 is the exponential
form of the number 125.
The Laws of Exponents:
#1: Exponential form: The exponent of a power indicates how
many times the base multiply itself.
x  x  x  x  x  x  x  x
n
n times
Example: 5  5  5  5
3
10 x 10 x 10 x 10 x 10 =
4 x 4 x 4 x 4 x 4 x 4 =
50 x 50 x 50 =
38 =
The Laws of Exponents:
#2: Multiplicative Law of Exponents: If the bases are the same
And if the operations between the bases is multiplication, then the
result is the base powered by the sum of individual exponents .
x x  x
m
n
mn
3 4
Example: 2  2  2  2
Proof: 23  24   2  2  2    2  2  2  2  
3
4
2222222  2
7
7
5
X
3
x
• (
2
7
5 •5 =(
)•(
)•(
)=
)=
The Laws of Exponents:
#3: Division Law of Exponents: If the bases are the same
And if the operations between the bases is division, then the
result is the base powered by the difference of individual
exponents .
m
x
m
n
mn

x

x

x
n
x
54
Example: 3  54  53  543  51  5
5
5
5
  5  5 5
Proof: 3 
5
5
5
 55
4
The Laws of Exponents:
#4: Exponential Law of Exponents: If the exponential form
is powered by another exponent, then the result is the base
powered by the product of individual exponents.
x 
n
m
Example:  4

3 2
Proof:  4
x
32
4
4
mn
6
   4  4  4   4  4  4   4  4  4 
3 2
 4  4  4  4  4  4  46
2
The Laws of Exponents:
#5: Product Law of Exponents: If the product of the bases
is powered by the same exponent, then the result is a multiplication
of individual factors of the product, each powered by the given
exponent.
 xy 
n
x y
n
n
Example: 36  6   2  3  2  3
2
Proof: 2  3  4  9  36
2
2
2
2
2
The Laws of Exponents:
#6: Quotient Law of Exponents: If the quotient of the bases
is powered by the same exponent, then the result is both
numerator and denominator , each powered by the given
exponent.
n
 x
x
   n
y
 y
n
3
2
 2
Example:    3
7
7
3
The Laws of Exponents:
#7: Negative Law of Exponents: If the base is powered by the
negative exponent, then the base becomes reciprocal with the
positive exponent.
x
m
1
 m
x
Example #1: 2
3
1
1
 3 
2
8
1
53
3
Example #2: 3 
 5  125
5
1
The Laws of Exponents:
#8: Zero Law of Exponents: Any base powered by zero exponent
equals one
x 1
0
Example: 1120  1
0
5
  1
7
 flower 
0
1